2023/07/11 by Jiajia Yang, Meng Jin, Xiangpeng Xin · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algorithm #Computer science #Conservation law #Dissipative system #Fractional Differential Equations Solutions #Geometry #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Symmetry (geometry) #Thermodynamics
paper · doi:10.1088/1402-4896/ace663
published in Physica Scripta 98(8), 085226 (IOP Publishing)
openalex publication_date 2023/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/13
Abstract The Lie symmetry analysis, optimal system, exact solutions and conservation laws of the (2+1)-dimensional variable-coefficients dissipative long-wave (vcDLW) system are introduced in this paper. Lie symmetry analysis method is used to obtain the vector field firstly. And the Olver <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo accent="false">′</mml:mo> <mml:mi mathvariant="normal">s</mml:mi> </mml:math> method is used to obtain the optimal system of one-dimensional subalgebras of the equations. Based on the optimal system, the equations are similarly reduced. Some representative equations are selected from the equations obtained after similarly reduction, and then the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>−</mml:mo> </mml:math> expansion method is applied to these equations, so that some new exact solutions of the (2+1)-dimensional vcDLW equations can be obtained. Finally, we study the conservation laws of the system.